Details of the agreement that ended the BART strike began to emerge shortly after trains started running again Tuesday morning -- and it quickly became clear that unions won big pay increases, while management scored key reforms to begin controlling medical and pension costs that have spiraled out of control.

A day after BART management and its two big unions announced the tentative contract, those involved with the talks said the death of two workers on the tracks Saturday finally pushed both sides to put aside their differences. In the days since the tragedy, both made significant concessions.

The terms of the deal have not been made public. But a notice sent to Amalgamated Transit Union workers, and confirmed to this newspaper by multiple sources, says the four-year contract calls for union employees to receive a 15.38 percent pay increase. That's only half a percentage point less than what unions wanted late last week and up from the 12 percent pay hike offered by BART before the strike. But it represented a compromise from management's initial offer to keep wages flat and unions' first proposal that amounted to a four-year equivalent of nearly 29 percent raises.

Currently, union workers make an average of $76,500 annually in gross pay, including overtime. The pay increase would push the average to $88,300 by 2017, though new rules will make it tougher to earn larger overtime checks.

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"The deal that we ended up getting quite honestly is not that much different from (unions') Friday" proposal, said Pete Castelli, executive director of the local Service Employees International Union. "We think it's a good deal and expect it to be ratified."

But management also won plenty of battles, including raising the employees' share of medical and pension benefits -- which will keep the net raise for workers relatively small. That was a key victory for rail line leaders: As BART has seen its rider and tax revenue counts surge to record levels, half of the $69 million in new revenue since 2010 has gone toward increased employee benefit costs.

Union workers, who do not currently contribute toward their pensions, will start contributing and ultimately pay 4 percent of pension costs by 2017. In June, unions had initially offered to pay just 0.5 percent, while management wanted 6 percent. The labor groups also agreed to management's proposal for worker bonuses. They will get $500 to $1,000 in one-time cash when annual rider counts exceed goals by 1 or 2 percent. Unions had wanted bigger and uncapped bonuses during flush times.

Workers' future health care payments, another key sticking point in the talks, will be going up from a flat $92 a month now to about $130, a compromise but mostly in line with BART's latest offer. BART, however, initially wanted workers to start paying a percentage of health care costs -- not the smaller, flat rates -- and had asked workers with multiple dependents to pay more.

BART also achieved its goal of eliminating a key provision that has allowed workers to earn large amounts of overtime. Historically, employees could call in sick one day, work four days and earn overtime on the fifth. Now, overtime pay will kick in only after employees work more than 40 hours a week.

Lt. Gov. Gavin Newsom, the highest-ranking official involved in facilitating the talks, said in an interview Tuesday that unions realized they were losing the public relations battle and that a prolonged strike would not help them. But, he said, management conceded that "if this ship sinks, regardless of who sunk it, we are all underwater" and finally moved from its "last, best and final" offer from a week before.

But Castelli, Newsom and others said the makings of a deal were put in motion after a "trainee" operating a train struck and killed the two workers on the tracks Saturday in Walnut Creek.

"My instincts tell me everyone just got fatigue on both sides and the tragedy was so emotive," said state Sen. Mark DeSaulnier, D-Concord, chairman of the state's transportation committee, who has been talking to each side for weeks.

Newsom added: "Both sides (said), 'Enough. We're past the point of excusing each other's actions and this impasse by pointing fingers -- we've got to get a deal.' "

Union officials said the accident served as the first confirmation that management was training new operators, which prompted unions to finally realize that BART management was intent on replacing workers if they stayed out on strike.

"The light bulb went off in our head: They never intended to make a deal," Castelli said. "They had the full intention of leaving us out there (on strike) and trying to run trains with replacement workers."

Castelli said some of the disputed "work rules" issues that have divided management and unions in the last week will be decided by an arbitrator, as the unions wanted. But he declined to discuss specifics.

Unions also said they would receive various safety upgrades and were hoping for the installation of bulletproof glass in 15 station agent booths.

"BART did a really good job on its PR -- they make the workers look really greedy," said Oakland Mayor Jean Quan, who was also involved in the talks. "But the (unions) were really serious about their safety issues."

BART management declined to discuss the deal until after it is approved by the rail line's board of directors and unions.

The board is set to discuss the contract in closed session Thursday morning. Castelli said union members will likely vote on the pact by early next week.